This thesis presents two new approaches in optical interferometry: phase difference determination by fringe pattern matching and a spatial phase-shifting interferometry (spatial PSI) algorithm. These two approaches are both theoretically described and experimentally illustrated in this thesis. The method of phase difference determination by fringe pattern matching is capable of detecting the phase difference between two interferograms with subpixel resolution. In this method, the phase curves are obtained from mean-square difference calculations of any two fringe patterns shifted pixel by pixel, and the phase difference between the interferograms can be achieved by linear interpolation or polynomial curve fitting from the phase curves. The signal to noise ratio is significantly improved due to the region-based matching and its effect of averaging noise. The equations derived from the statistical analysis of matching process clearly explain the reason that the larger image patches have a better accuracy in the measurement of phase difference. The three applications of fringe pattern matching, measurement of electrostatic force displacement, displacement measurement based on Youngs experiment, and phase-shifting interferometry with arbitrary phase steps, are also investigated in this thesis. Computer simulation and experimental results have proved that fringe pattern matching is a powerful technique for measuring some basic parameters in optical interferometry such as phase difference, fringe spacing and displacement. In the algorithm of spatial PSI, one fringe pattern is captured by a CCD camera, and the other two shifted fringe patterns with the phase steps of 90oC and 180oc are generated by computer, according to the features of the light intensity distributions and the method of interpolation. The phase is then calculated by a standard three-step algorithm of phase-shifting interferometry. Experimental results have shown that it is a useful approach to spatial PSI.